We propose that the entropy of de Sitter space can be identified with the mutual entropy of a dual conformal field theory. We argue that unitary time evolution in de Sitter space restricts the total number of excited degrees of freedom to be bounded by the de Sitter entropy, and we give a CFT interpretation of this restriction. We also clarify issues arising from the fact that both de Sitter an...

We introduce a self-dual field strength which replaces the gauge field in spontaneously broken Yang-Mills theory, reformulating it as a Lorentz covariant non-linear sigma model. This dualized theory is in both a unitary and renormalizable gauge: The self-dual field strength has exactly the three components necessary to describe a massive vector field. In future work we shall utilize this new fo...

We investigate a class of brickwork-like quantum circuits on chains $d-$level systems (qudits) that share the so-called `dual unitarity' property. Namely, these generate unitary dynamics not only when propagating in time direction, but also space direction. consider space-time homogeneous (Floquet) and perturb them with quenched single-site disorder, i.e. by applying independent single site ran...

A class of mathematical dualities have played a central role in mapping states in gauge theory to states in the spacetime string theory dual. This includes the classical Schur-Weyl duality between symmetric groups and Unitary groups, as well as generalisations involving Brauer and Hecke algebras. The physical string dualities involved include examples from the AdS/CFT correspondence as well as ...

Theta correspondence y over R is established by Howe (J. Amer. Math. Soc. 2 (1989) 535). In He (J. Funct. Anal. 199 (2003) 92), we prove that y preserves unitarity under certain restrictions, generalizing the result of Li (Invent. Math. 97 (1989) 237). The goal of this paper is to elucidate the idea of constructing unitary representation through the propagation of theta correspondences. We show...

We consider one-dimensional quantum circuits of the brickwork type, where fundamental gate is dual unitary. Such models are solvable: dynamical correlation functions infinite temperature ensemble can be computed exactly. review various existing constructions for unitary gates and we supplement them with new ideas in a number cases. discuss connections topics physics mathematics, including infor...

If the locally compact abelian group G has a finitedimensional unitary irreducible projective representation with factor system co (i.e. G has an a>-rep), then a subgroup G(co) is defined which fulfils three roles. First, the square-root of the index of G(u)) in G is the dimension of every co-rep. Secondly, the co-reps of G can be labelled by the dual group of G(co), up to unitary equivalence. ...

In this paper we consider the problem of decomposing tensor products of certain singular unitary representations of a semisimple Lie group G. Using explicit models for these representations (constructed earlier by one of us) we show that the decomposition is controlled by a reductive homogeneous space G′/H′. Our procedure establishes a correspondence between certain unitary representations of G...